The picture fuzzy set is an extension of the fuzzy and intuitionistic fuzzy set for solving real-world problems. Entropy and distance measures play significant roles in measures for solving problems involving fuzzy environments. This paper has presented some new distance and entropy measures using picture fuzzy sets to solve problems of medical diagnosis and multi-criteria decision making problems. In addition, the entropy measure is induced from the distances of picture fuzzy sets in order to determine entropy measure of picture fuzzy sets. The proposed methods combined entropy and distance measures to construct the Technique for Order of Preference by Similarity to Ideal Solution model to solve multi-criteria decision making problem. To validate the proposed methods, some numerical examples are given to demonstrate new measurements. The efficiency of the measure is proven by comparison to other measures when solving medical diagnosis in multi-criteria decision making for illustrations in numerical COVID-19 medicine selection.

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